This paper describes a nev probabilistic roadmap (PRM) path planner that is: (1) single-query instead of pre-computing a roadmap covering the entire free space, it uses the tvo input query configurations as seeds to explore as little space as possible; (2) hi-directional it explores the robotis free space by concur- rently building a roadmap made of tvo trees rooted at the query configurations; (3) adaptive it makes longer steps in opened areas of the free space and shorter steps in cluttered areas; and (4) lazy in checking collision it delays collision tests along the edges of the roadmap until they are absolutely needed. Experimental results shov that this combination of techniques drastically reduces planning times, making it possible to handle difficult problems, including multi-robot problems in geometrically complex environments.

In a geometric context, a collision or proximity query reports information about the relative configuration or placement of two objects. Some of the common examples of such queries include checking whether two objects overlap in space, or whether their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries. Hundreds of papers have been published on di#erent aspects of these queries in computational geometry and related areas such as robotics, computer graphics, virtual environments, and computer-aided design. These queries arise in di#erent applications including robot motion planning, dynamic simulation, haptic rendering, virtual prototyping, interactive walkthroughs, computer gaming, and molecular modeling. For example, a large-scale virtual environment, e.g., a walkthrough, creates a model of the environment with virtual objects. Such an environment is used to give the user a sense of presence in a synthetic world and it s

We consider the problem of preprocessing a scene of polyhedral models in order to perform collision detection very efficiently for an object that moves amongst obstacles. This problem is of central importance in virtual reality applications, where it is necessary to check for collisions at real-time rates. We give an algorithm for collision detection that is based on the use of a mesh (tetrahedralization) of the free space that has (hopefully) low stabbing number. The algorithm has been implemented and tested, and we give experimental results comparing its performance against three other algorithms that we implemented, based on standard data structures. A preliminary version of this paper appeared in the proceedings of the 7 th Canad. Conf. Computat. Geometry, Qu'ebec, Aug 10--13, 1995. y held@ams.sunysb.edu; Supported by NSF Grant DMS-9312098. On sabbatical leave from Universitat Salzburg, Salzburg, Austria. z jklosow@ams.sunysb.edu; Supported by NSF grants ECSE-8857642 and C...

This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query -- instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional -- it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions -- it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques, and those of delayed collision checking reinforce each other. Experimental results

In this paper we present a framework for minimum distance computations that allows efficient solution of minimum distance queries on a variety of surface representations, including sculptured surfaces. The framework depends on geometric reasoning rather than numerical methods and can be implemented straightforwardly. We demonstrate performance that compares favorably to other polygonal methods and is faster than reported results for other methods on sculptured surfaces. 1 Introduction We introduce a framework for minimum distance calculations that applies well to both polygonal and parametric model representations (Figure 1). The resulting methods scale well with problem size, have time-critical properties, and are interactive for large polygonal models and sculptured surfaces. In robotics, minimum distance queries have been used in path planning [2], path modification [25], and collision avoidance [15]. In computer graphics, minimum distance computations have played roles in physical...

The traditional high-level algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies. The problem is unnecessary synchronization implicit in these methods. Jefferson´s timewarp algorithm (Jefferson 85) is a technique for alleviating this problem in parallel discrete event simulation. Rigid body dynamics, though a continuous process, exhibits many aspects of a discrete one. With modification, the timewarp algorithm can be used in a uniprocessor rigid body simulator to give substantial performance improvements for simulations with large numbers of bodies. This paper describes the limitations of the traditional high-level simulation algorithms, introduces Jefferson´s algorithm, and extends and optimizes it for the rigid body case. It addresses issues particular to rigid body simulation, such as collision detection and contact group management, and describes how to incorporate these into the timewarp framework. Quantitative experimental results indicate that the timewarp algorithm offers significant performance improvements over traditional high-level rigid body simulation algorithms, when applied to systems with hundreds of bodies. It also helps pave the way to parallel implementations, as the paper discusses.

Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physically-based modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are used to test for interference orcompute distance bounds between the underlying geometry. The e ciency of a hierarchy is directly proportional to the choice ofabounding volume. In this paper, we introduce spherical shells, a higher order bounding volume for fast proximity queries. Each shell corresponds to a portion of the volume between two concentric spheres. We present algorithms to compute tight tting shells and fast overlap between two shells. Moreover, we show that spherical shells provide local cubic convergence to the underlying geometry. As aresult, in many cases they provide faster algorithms for interference detection and distance computation as compared toearlier methods. We also describe an implementation and compare it with other hierarchies. 1

We introduce the boxtree, a versatile data structure for representing triangulated or meshed surfaces in 3D. A boxtree is a hierarchical structure of nested boxes that supports efficient ray tracing and collision detection. It is simple and robust, and requires minimal space. In situations where storage is at a premium, boxtrees are effective alternatives to octrees and BSP trees. They are also more flexible and efficient than R-trees, and nearly as simple to implement. Keywords: collision detection, hierarchical data structures, ray shooting. 1. Introduction In 1981 Ballard 1 presented a simple data structure for representing digitized curves by means of nested strips. This work is an attempt to generalize his strip tree structure to the case of surfaces in 3D. As is well known, curves can seem quite tame when compared to surfaces. For example, collision detection in 3D is orders of magnitude more difficult than in 2D. Expectedly, generalizing a strip tree into a boxtree raises a ...

This paper introduces a fast continuous collision detection technique for polyhedral rigid bodies. As opposed to most collision detection techniques, the computation of the first contact time between two objects is inherently part of the algorithm. The method can thus robustly prevent objects interpenetrations or collisions misses, even when objects are thin or have large velocities. The method is valid for general objects (polygon soups), handles multiple moving objects and acyclic articulated bodies, and is efficient in low and high coherency situations. Moreover, the method can be used to speed up existent continuous collision detection methods for parametric or implicit rigid surfaces. The collision detection algorithms have been successfully coupled to a real-time dynamics simulator. Various experiments are conducted that show the method’s ability to produce high-quality interaction (precise objects positioning for example) between models up to tens of thousands of triangles, which couldn’t have been performed with previous continuous methods. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Animation- Virtual Reality 1.

: We present new distance computation algorithms using hierarchies of rectangular swept spheres. Each bounding volume of the tree is described as the Minkowski sum of a rectangle and a sphere, and fits tightly to the underlying geometry. We present accurate and efficient algorithms to build the hierarchies and perform distance queries between the bounding volumes. We also present traversal techniques for accelerating distance queries using coherence and priority directed search. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms have achieved significant speedups on many benchmarks. 1